N-category Theory

N-category theory is a branch of mathematics that studies abstract structures called "categories," which consist of objects and the relationships (called morphisms) between them. It generalizes the idea of mathematical systems by allowing multiple levels of relationships—morphisms between morphisms, and so on—up to any number of layers (N levels). This framework helps mathematicians understand complex interconnected structures across different areas, such as algebra, topology, and logic, by focusing on how structures relate and compose, revealing deep connections and patterns within mathematics itself.